Summer Math Research Program

This is the website for the Northeastern Summer Math Research Program (NSMRP), a paid summer program funded by the math department's Research Training Grant.

Other undergraduate math research opportunities at Northeastern.

Research Experience for Undergraduates

REU 2024

This program is only for Northeastern students

Calendar

More information for undergraduates participants 

More information for mentors 

Research projects and mentors

Participants: Ang Barrett, Daniel Kiem, and Mitchell Wadas

Faculty mentor: Harm Derksen

Graduate student mentor: Shengnan Huang

Participants: Zachary Greenfield, Jonah Marcus, and Jordan Martino

Graduate student mentors: Sean Carroll and Vitor Gulisz

Participants: Aden Lu and Roland Waterson

Graduate student mentor: Yujia Shi

Participants: Aidan Tillman and Yuzhi Liu

Faculty mentor: Stuart Brorson

Graduate student mentor: Zhaoming Li

Participants: Jacob Ginesin and Daniel Yu

Faculty mentor: David Rosen

Graduate student mentors: Forrest Miller

Participants: Walla Rahama and Ishan Thakur

Faculty mentor: Milen Yakimov

Graduate student mentor: Yunmeng Wu

Participants:  Devin Brown, Emily Fink, and Naiwen Wang

Faculty Mentor: Vance Blankers

Graduate student mentor: Rahul Hirwani

Participants: Abby Jiang and Nicholas Sokolovic

Graduate student mentor: Arturo Ortiz San Miguel

Post-doc coordinators: Hunter Dinkins and Josh Wen

Faculty organizers: Harm Derksen, Iva Halacheva, Valerio Toledano Laredo, and Xuwen Zhu

REU 2023

Additional funding for the Summer 2023 program was provided by the College of Science and Department of Mathematics.

Research projects and mentors

Participants: Tao (Luisa) Li, Aaron Soice, and Ryan Zhu

Mentor: Olakunle Abawonse

Paper: Group equivariant neural networks 

Final presentation slides

Participants: Evelyn Brylow, Timothy Demling, Walla Rahama, and Nicholas Sokolovic

Mentors: Sean Carroll and Hunter Dinkins

Paper: P-adic numbers 

Final presentation slides

Chemical reaction networks and monotone dynamical systems

Participants: Edward Berman and Anna XiaMentor:  Alon DuvallAffiliated faculty: Eduardo D. Sontag and M. Ali Al-RadhawiPaper: Sufficient conditions for monotonicity in stochastic chemical reaction networks 

Final presentation slides

Participants: Devin Brown, Daniel Kiem, and Jordan Martino

Mentor: Shengnan Huang

Affiliated faculty: Milen Yakimov

Paper: Combinatorial construction of nilpotent Lie algebras 

Final presentation slides

Participants: Zachary Greenfield and Zoey Yelsky

Mentor: M. Anadil Saeed Rao

Paper: Representations of the Virasoro algebra 

Final presentation slides

Participants: Jonah Marcus and Molly Sager

Mentor: Ahmad Reza Haj Saeedi Sadegh

Paper: Schwartz functions and compactifications 

Final presentation slides

Post-doc coordinator: Josh Wen

Faculty organizers: Iva Halacheva, Valerio Toledano Laredo, and Xuwen Zhu

REU 2022

In light of the COVID-19 pandemic, this program was held remotely.

Research projects and mentors

Equivalent matroids arising from graphs

Participants: Jiaqi Lu and Brandon Onyejekwe Mentor:  K. Finn PrideauxPaper: Equivalent matroids arising from graphsFinal presentation slides

Morita theorems

Participants: Nicholas Bidorini and Zach Greenfield 

Mentor: Vitor Emanuel Gulisz

Paper: The Morita theorems 

Final presentation slides

Regularization and renormalization in quantum field theory

Participants: Daniel Abadjiev, Anthony Melo, and Zhengxun Liu

Mentor: M. Anadil Saeed Rao

Paper: Renormalization and regularization of φ^4 and φ^3 scalar quantum field theories 

Final presentation slides

Graph bootstrap percolation

Participants: Andy Babb, Stephanie Martinez, and Timothy Wang

Mentor: Connor Anderson

Paper: Approximation of spread minimization in bootstrap percolation 

Final presentation slides

Knot polynomials and Khovanov homology

Participants: Jordan Martino and Francisco Turdera

Mentor: Ryan Kannanaikal

Paper: Knot polynomials and Khovanov homology 

Final presentation slides

Post-doc coordinators: Iva Halacheva, Matej Penciak, Josh Wen

Faculty organizer: Valerio Toledano Laredo 

REU 2021

In light of the COVID-19 shutdown, this program was held entirely remotely. 

Additional funding for the Summer 2021 program was provided by the College of Science and Department of Mathematics.

Calendar


Final Paper: The jointly written paper should be at least 10 pages. Should include an introduction with motivation and guiding questions, definitions, examples, a main result and proof. No maximum page limit, but writing should be clear and concise.

Final Presentation: (45 for each group) Should introduce audience to area of research, convince them it is interesting through examples, definitions and results. Time is too short to include everything so choose carefully what to present highlighting what you worked hardest on. Narrative and slides and/or boardwork should be clear.

More information for Undergraduate participants.  

More information for Graduate mentors.

Groups

Configuration spaces of points and lines

Participants: Luke Boyer, Shane Calle, Nick Payne.  Mentor: Ian Dumais 

Paper: Configurations of Lines and Spaces

Probabilistic simulations of IOTA cryptocurrency

Participants: Maria Candello, Grant Chau, Jiachen Xu.  Mentor: Anupam Kumar

Paper: Probabilistic Simulations of IOTA Cryptocurrency

Modeling of random geometric graphs  

Participants: Maitreyee Joshi, Nicholas Thevenin, Bryan Vogt.  Mentor: Hiu Ying Man

Paper: Extending Bottleneck Matching and Monotone Property Threshold Width to the Torus

Chromatic numbers of fractional power graphs  

Participants: Luke Drennen, Noah Lichtblau.  Mentor: Finn Prideaux

Paper: Chromatic Numbers and K-Connectivity of Graph Fractional Powers


Post-doc coordinators: Vance Blankers, Matej Penciak

Faculty organizer: Valerio Toledano Laredo 

REU 2020

In light of the COVID-19 shutdown, this program was held entirely remotely. 

Calendar


Final Paper: The jointly written paper should be at least 10 pages.   Should include an introduction with motivation and guiding questions, definitions, examples, a main result and proof.  No maximum page limit, but writing should be clear and concise.

Final Presentation:  (45 for each group).   Should introduce audience to area of research, convince them it is interesting through  examples, definitions and results.  Time is too short to include everything so choose carefully what to present highlighting what you worked hardest on.   Narrative and slides and/or boardwork should be clear.

More information for Undergraduate participants.  

More information for Graduate mentors.

Groups

Evolutionary Dynamics.  

Participants: Jack Steilberg, Lauren Neudorf.  Mentor: Jonier Antunes. 

Paper: Infinite Random Graphs and Evolutionary Dynamics

Spectral Graph Theory.

Participants: Ryan Keleti, Noble Mushtak.   Mentor: Whitney Drazen. 

Paper: Fractional Revival and Fractional Cospectrality

Elliptic Curves.

Participants: Zoe Daunt, Xiaoying He, Xuyang Li.   Mentor: Lei Yang.

Paper: Elliptic Curves and Probability of $\ell$-torsion


Post-doc coordinators: Rob Silversmith, Robin Walters

Faculty organizer: Valerio Toledano Laredo 

REU 2019

Calendar


Final Paper: At least 5 pages.  If two students, then paper is written together is at least 10 pages.   Should include an introduction with motivation and guiding questions, definitions, examples, a main result and proof.  No maximum page limit, but writing should be clear and concise.

Final Presentation:  30 minutes (40 if group of 2).   Should introduce audience to area of research, convince them it is interesting through  examples, definitions and results.  Time is too short to include everything so choose carefully what to present highlighting what you worked hardest on.   Narrative and slides and/or boardwork should be clear.

More information for Undergraduate participants.  

More information for Graduate mentors.





Groups

Evolutionary Dynamics.  

Participants: Hoyin Chu.  Mentor: Jonier Antunes.  Summer I. 

Paper: Introduction to Evolutionary Dynamics and Stochastic Calculus.

Knot Theory.

Participants: Noah Fleischmann, Kally Lyonnais.   Mentor: Dmytro Matvieievsky.  Summer I.

Paper: Knots, Colors, and Polynomials.

Graph Theory/Chip Firing:

Participants: Kristin Timothy, Michael Wang.   Mentor: Ian Dumais. Summer I.

Paper: Sandpiles and Chip Firing.

Homotopical Algebra:

Participants: Karthik Boyareddygari   Mentor: Oleksiy Sorokin. Summer I.

Paper: Homotopical Approach to Tensor Products.

Algebraic Geometry:

Participants: Walker Miller-Breetz.  Mentor: Anupam Kumar.  Summer II.

Paper: Cone Points on Algebraic Curves.


Post-doc coordinators: Emily Barnard, Rob Silversmith, Robin Walters

Faculty organizer: Valerio Toledano Laredo 

REU 2018

The inaugural year of the Northeastern REU had 9 undergraduate participants working in several different areas.   The postdoc coordinator was Ivan Martino.

Mentor: Brian Hepler 

Title: Abstract Regular Polytope

Abstract: Introduction to Abstract Regular Polytopes through a combinatorial geometry approach. C-Groups, Coxeter Groups and 2^k-constructions are also studied.


Mentor: Jonier Antunes 

Title: Graph Limits and Extremal Combinatorics

Abstract: "One of the problems in extremal combinatorics is asking how many edges a graph on n nodes may have while avoiding some specific subgraphs. For example, Mantel’s theorem says that the most edges a graph on n nodes can have while avoiding K_3 is n^2/4. These statements can also be represented in terms of inequalities of numbers of homomorphisms or in terms of homomorphism densities. Many of these inequalities may be proved using Cauchy-Schwarz (as an inequality on sums of squares) or pictorially due to a gluing algebra on the space of graphs. We summarize some of the graph algebra background involved here and look at how graph limit theory gives a way of proving results in extremal combinatorics."


Mentor: Whitney Drazen

Title: Graph Theory

Abstract: This is an introduction to spectral graph theory until the concepts of (quantum) state transfer.


Mentor: Alex Sorokin

Title: Leavitt Path Algebras 

Abstract. We describe different properties of Leavitt path algebras of a graph over a field, providing the appropriate background. In addition, we investigate similar results about Leavitt path algebras of a graph over a commutative unital ring. We will mainly explore the connection between the diagonalizability of matrices over a given Leavitt path algebra and the structure of its underlying graph, as well as the classification of such algebras up to isomorphism.


Mentor: Reuven Hodges 


Mentor: Rahul Singh 

Title: Young Tableaux 

Abstract: After a short introduction on group theory and group actions, the work focuses on the symmetric group and its action on flagged spaces.


Mentor: Whitney Drazen

Title: Non-backtracking Walks on Graphs

Abstract: The main goal of the REU was to obtain a new proof of the non-backtracking version of Ploya’s Theorem for random walks. We began with a discussion of spectral graph theory before studying the backtracking version of Ploya’s Theorem.


Mentor: Mikhail Mironov

Title: On the Morphism of Schemes


Mentor: Celine Bonandrini

Title: Topology


Image credit: Tom Ruen, Jaap Scherphuis’s Tiling Viewer, Robert Webb's Stella

Calendar

More information for Undergraduate participants.  

More information for Graduate mentors.